When explaining stuff to him, make sure he understands how you're doing a problem. Steps that might be incredibly simple for you might confuse him. I'd also recommend that you have him explain why you/him are doing the things you do. He might just be following a pattern, which might work sometimes, but not all of the time.

One of the things that has confused one of the students I've tutored is distributing a negative sign. Your cousin probably doesn't have a problem with that, but I'd make sure he doesn't cause that's something that can screw you up even in higher maths like calculus.posted by kylej at 9:02 AM on November 7, 2009

Start by doing lots of practice problems together. If he doesn't know something...don't give it to him but don't make him so frustrated he's going to scream. Tell him the answer and explain it. Go through every step and explain it so he understands. Then, after you've done problems where you've taken the lead let him solve some problems. Start with easier ones and then advance up. Once he's done solving the problems get him to explain them to you and to teach them to you. So not only do problems with him but have him explain them to you as well.

Good luck! I find teaching to be hard...posted by lucy.jakobs at 9:30 AM on November 7, 2009

Make sure he knows arithmetic. People I tutored didn't have trouble with the algebra part, they had trouble with multiplication and division and negative numbers.posted by jeather at 9:45 AM on November 7, 2009

This trick helped me, a 30-ish adult suffering through college algebra, with negative numbers. I'd draw a horizontal line and call its center point zero. It was a sort of thermometer: positive to the left, negative to the right. I could use it to visualize the problem much more easily.posted by Carol Anne at 10:09 AM on November 7, 2009

For three years now, I have been tutoring in Algebra and Pre-Calculus at a local community college.

My biggest word of advice is to be consistent. Try to establish a pattern in how problems are set up and simplified. Try to build a sense of expectation and intuition in your cousin that, "If I do 'this', I should see something like 'that' happen."

Try to build upon previous lessons. Things you learn in graphing lines should be your reference points when learning to graph parabolas, should be your foundation for graphing exponential functions.

Be patient. The best thing I ever heard an instructor say was, "Does this make sense? Do you see the pattern yet? If you don't, don't worry. We'll keep doing examples until it all makes sense." That idea that we had plenty of time and he was going to keep covering the material until everyone "got it" was hugely reassuring.posted by browse at 10:12 AM on November 7, 2009 [3 favorites]

Things I had to learn about tutoring by experience:

Try extra hard not to be intimidating. Your student thinks you are smart and wants you to think he is smart. You need to make him feel safe about making mistakes. Otherwise he'll freeze up and make you do all the work.

Some people listen better than they read; some people read better than they listen. Instead of writing the problem and speaking the explanation, which was what came naturally to me, both write and speak everything. Write an explanation of the problem alongside the problem itself. And draw pictures!

It's tempting to hold the student's hand too much. Make sure your student can actually do a problem on his own, with no prompts from you (but notes are ok) before you move on to another concept. It's ok to sit there doing nothing while he works, but even better if you can invent a task for yourself to keep out of his hair. Make sure you have plenty of practice problems ready, or get good at writing them on the spot.

He needs to practice on his own too. Give him some structure for that, but make sure he doesn't perceive it as onerous. Ask how much work he'd be willing to do every single day, and give him that much work to do.

When you're building on a concept that he really should know already-- say, what an exponent means-- assume nothing. Drop in plenty of parentheticals like "you remember what 'squared' means?" or "You remember PEMDAS?"

I started writing a bunch of algebra-specific stuff, but I don't really know much about the Regents exam, and your link doesn't seem to work. Feel free to PM me if you want more advice.posted by molybdenumblue at 11:15 AM on November 7, 2009 [2 favorites]

The nice thing about algebra is that a lot of it has a geometric interpretation. If you can present the same thing in a couple of different ways, or an idea with a bunch of different motivating examples, perhaps that will help?

One of the easiest ways for me to learn something is to see a wide range of examples worked through, keep those as reference, and then do problems starting from questions very similar to the examples (different numbers, different expressions, etc but the same setup) and gradually move up to problems that synthesize material from the examples & make you apply it differently. This takes a lot of effort on the part of the instructor, but it has always been a way for me to pick something up without feeling like I'm really exerting myself.posted by devilsbrigade at 11:42 AM on November 7, 2009 [2 favorites]

Teach him to him maintain good practices, like writing down what each word problem variable represents, including each step when simplifying equations, formating Cramer's rule related equations correctly, etc. so he's rock solid on fundamentals when doing harder work. Knowing that they know the tools can give kids the patience and confidence they need to plow through more difficult work. If he pretends that he's explaining it to someone else or that someone will review the work who needs to see every step, that may help; too often kids either see or intuit the answer/next step and so they don't absorb technique.posted by carmicha at 3:14 PM on November 7, 2009 [1 favorite]

The regents is sort of a bitch. On your end I would suggest looking at a few practice tests/sample questions just to get an idea of the very specific way the problems are presented in the test.posted by saxamo at 7:18 PM on November 7, 2009 [1 favorite]

Thanks for all the responses--some great insights here.posted by dfriedman at 1:43 PM on November 8, 2009

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